This inequality permits to give an upper bound for the discrepancy of a sequence of elements in \(\mathbb {R}^s\)  in terms of finitely many trigonometrical sums. The case when \(s=1\)  has been given by Erdős and Turán in [1]} and generalized to higher dimensions independently by Koksma [2]} and Szüsz [3]}. We quote here the formulation given by Drmota and Tichy [4]}. We first recall the definition of the discrepancy.
